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How do you find f'(x) using the definition of a derivative for #f(x)=e^x #?

1 Answer

Konstantinos Michailidis

Sep 25, 2015

Refer to explanation

Explanation:

The definition of the first derivative is

#f'(x)=lim_(h->0) (f(x+h)-f(x))/(h)#

hence for #f(x)=e^x# we have that

#f'(x)=lim_(h->0) (e^(x+h)-e^x)/h=lim_(h->0) e^x*((e^h-1)/h)= e^x*lim_(h->0)((e^h-1)/h)=e^x#

Remarks

#lim_(h->0) ((e^h-1)/h)=1#

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